E.N. Sabziev
Algorithm for determining the trajectory of maneuvers along the planned route on a geometric map of the terrain

The paper considers the problem of calculating the trajectory of an unmanned aerial vehicle based on a geometric map, where obstacles and undulations of the terrain are specified in the form of spheres. A mathematical model for calculating the optimal trajectory is constructed, which, under additional smoothness conditions, is reduced to a boundary value problem for a system of nonlinear second-order differential equations. For practical purposes, a heuristic algorithm is proposed for the numerical calculation of one of the possible rational trajectories, which allows the drone to fly around obstacles with a minimum number of changes in the flight mode.

Keywords: Unmanned aerial vehicle, Geometric map, Optimal trajectory, Differential equation, Heuristic algorithm
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